Let the radius of a circle be r.
∴ Circumference of a circle =2πr
Let the radii of two circles are r1 and r2 whose values are 15 cm and 18 cm, respectively .
⇒ r1=15 cm, r2=18 cm
Now, by given condition,
Circumference of circle = Circumference of first circle + Circumference of second circle
⇒2πr=2πr1+2πr2
⇒r=r1+r2
⇒r=15+18
∴r=33 cm
Hence, required radius of a circle is 33 cm.